Lemma 1.2 ([1]}) 
Let \( B_0 \subset B \subset B_1 \)  be Banach spaces, \( B_0 \)  and \( B_1 \)  reflexive, with compact embedding of \( B_0 \)  in \( B \) .
Let \( p \in (1,\infty ) \)  and \( \alpha \in (0,1) \)  be given.
Let \( X \)  be the space
\(X = L^p(0,T; B_0) \cap W^{\alpha ,p}(0,T;B_1)\) 
